Optimal. Leaf size=17 \[ \frac{6}{5} \left (x-3 \sqrt{x}\right )^{5/3} \]
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Rubi [A] time = 0.0845331, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 28, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.071 \[ \frac{6}{5} \left (x-3 \sqrt{x}\right )^{5/3} \]
Antiderivative was successfully verified.
[In] Int[((-3 + 2*Sqrt[x])*(-3*Sqrt[x] + x)^(2/3))/Sqrt[x],x]
[Out]
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Rubi in Sympy [A] time = 6.32127, size = 14, normalized size = 0.82 \[ \frac{6 \left (- 3 \sqrt{x} + x\right )^{\frac{5}{3}}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((x-3*x**(1/2))**(2/3)*(-3+2*x**(1/2))/x**(1/2),x)
[Out]
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Mathematica [A] time = 0.0212846, size = 17, normalized size = 1. \[ \frac{6}{5} \left (x-3 \sqrt{x}\right )^{5/3} \]
Antiderivative was successfully verified.
[In] Integrate[((-3 + 2*Sqrt[x])*(-3*Sqrt[x] + x)^(2/3))/Sqrt[x],x]
[Out]
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Maple [A] time = 0.013, size = 12, normalized size = 0.7 \[{\frac{6}{5} \left ( x-3\,\sqrt{x} \right ) ^{{\frac{5}{3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((x-3*x^(1/2))^(2/3)*(-3+2*x^(1/2))/x^(1/2),x)
[Out]
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Maxima [A] time = 0.946612, size = 24, normalized size = 1.41 \[ \frac{6}{5} \,{\left (x^{\frac{4}{3}} - 3 \, x^{\frac{5}{6}}\right )}{\left (\sqrt{x} - 3\right )}^{\frac{2}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x - 3*sqrt(x))^(2/3)*(2*sqrt(x) - 3)/sqrt(x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.305304, size = 15, normalized size = 0.88 \[ \frac{6}{5} \,{\left (x - 3 \, \sqrt{x}\right )}^{\frac{5}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x - 3*sqrt(x))^(2/3)*(2*sqrt(x) - 3)/sqrt(x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.90253, size = 36, normalized size = 2.12 \[ - \frac{18 \sqrt{x} \left (- 3 \sqrt{x} + x\right )^{\frac{2}{3}}}{5} + \frac{6 x \left (- 3 \sqrt{x} + x\right )^{\frac{2}{3}}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x-3*x**(1/2))**(2/3)*(-3+2*x**(1/2))/x**(1/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (x - 3 \, \sqrt{x}\right )}^{\frac{2}{3}}{\left (2 \, \sqrt{x} - 3\right )}}{\sqrt{x}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x - 3*sqrt(x))^(2/3)*(2*sqrt(x) - 3)/sqrt(x),x, algorithm="giac")
[Out]